Rational Number Theory in the 20th Century PDF Download

Author: Władysław Narkiewicz
Publisher: Springer Science & Business Media
ISBN: 0857295322
Category : Mathematics
Languages : en
Pages : 659

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Book Description
The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.

Author: Władysław Narkiewicz
Publisher: Springer
ISBN: 3030037541
Category : Mathematics
Languages : en
Pages : 448

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Book Description
The book is aimed at people working in number theory or at least interested in this part of mathematics. It presents the development of the theory of algebraic numbers up to the year 1950 and contains a rather complete bibliography of that period. The reader will get information about results obtained before 1950. It is hoped that this may be helpful in preventing rediscoveries of old results, and might also inspire the reader to look at the work done earlier, which may hide some ideas which could be applied in contemporary research.

Author: Purabi Mukherji
Publisher: Springer Nature
ISBN: 9811596204
Category : Mathematics
Languages : en
Pages : 187

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Book Description
This book is an attempt to describe the gradual development of the major schools of research on number theory in South India, Punjab, Mumbai, Bengal, and Bihar—including the establishment of Tata Institute of Fundamental Research (TIFR), Mumbai, a landmark event in the history of research of number theory in India. Research on number theory in India during modern times started with the advent of the iconic genius Srinivasa Ramanujan, inspiring mathematicians around the world. This book discusses the national and international impact of the research made by Indian number theorists. It also includes a carefully compiled, comprehensive bibliography of major 20th century Indian number theorists making this book important from the standpoint of historic documentation and a valuable resource for researchers of the field for their literature survey. This book also briefly discusses the importance of number theory in the modern world of mathematics, including applications of the results developed by indigenous number theorists in practical fields. Since the book is written from the viewpoint of the history of science, technical jargon and mathematical expressions have been avoided as much as possible.

Author: Franz Halter-Koch
Publisher: CRC Press
ISBN: 1466591846
Category : Mathematics
Languages : en
Pages : 431

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Book Description
Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic setting, the author focuses on equivalence, continued fractions, quadratic characters, quadratic orders, binary quadratic forms, and class groups.T

Author: Michael Th. Rassias
Publisher: Springer Science & Business Media
ISBN: 1441904956
Category : Mathematics
Languages : en
Pages : 336

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Book Description
The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).

Author: RAJ SHREE DHAR
Publisher: Mohini publications
ISBN:
Category : Antiques & Collectibles
Languages : en
Pages : 97

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Book Description
This book is an attempt to explain the human endeavor concerning evolution and development of Mathematics through the millennia. One of the essential importance of this book is to bring out in a humble way the indispensability of Mathematics in modern life. It is essential as a matter of simple survival for us to understand and professionalize Mathematics in our day to day life. Last Chapter is about Women Mathematicians. The idea behind this is to attract more and more women for future development of Mathematics. The author invites suggestions which could be considered for the improvement of the subsequent editions of this work.

Author: Prof. Jyothi M. J.
Publisher: RK Publication
ISBN: 9348020080
Category : Mathematics
Languages : en
Pages : 282

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Book Description
Number Theory is a comprehensive exploration of the foundational concepts, theorems, and applications in number theory. Prime numbers, congruences, and Diophantine equations, offering both classical insights and modern perspectives. It caters to a broad audience, from students to advanced mathematicians, with a focus on problem-solving, proofs, and historical context. Rich with examples, exercises, and applications, Number Theory illuminates the subject's intrinsic beauty and its significance in fields like cryptography, computer science, and mathematical research.

Author: Nicholas Faulkner
Publisher: Encyclopaedia Britannica
ISBN: 1538300427
Category : Juvenile Nonfiction
Languages : en
Pages : 296

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Book Description
This comprehensive volume is perfect for students who are interested in higher-level study of numbers and measurements. The book delves into the history of mathematical reasoning and the progression of numerical thought. Readers will learn how our world is shaped by the number and measurement systems that have arisen over time. They will also engage in the history of the development of number and measurement systems and the biographies of some of the greatest mathematical minds throughout history. This is a perfect volume for anyone interested in higher-level math and the stories behind it.

Author: Israel Kleiner
Publisher: Springer Science & Business Media
ISBN: 0817682686
Category : Mathematics
Languages : en
Pages : 362

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Book Description
This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work. Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses.

Author: Sivaramakrishnan R
Publisher: CRC Press
ISBN: 1420015060
Category : Mathematics
Languages : en
Pages : 660

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Book Description
Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutati